Numbers 2
1) A number leaves a remainder of 10 when divided by 18. What is the remainder when the same number is divided by 3?
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2) What is the sum of the remainders we get when 4735781 is divided by each of 2, 3, 4, 5, 8 and 9?
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3) What is the product of the remainders we get when 8657925 is divided by each of 7, 11, 13, 19, 20 and 25?
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4) What is the largest possible number that divides 37, 75 and 115 with remainders of 1, 3 and 7 respectively?
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5) How many different positive integers would divide 37, 85 and 109 and leave the same remainder?
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6) What is the second smallest positive integer which would leave a remainder of 3 when divided by 5, 6 or 8?
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7) What is the fourth smallest positive integer which, when successively divided by 3, 5 and 6, would leave remainders of 1, 3 and 4 respectively?
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8) What is the remainder when (3748 + 2779) × (5865 - 4871) is divided by 9?
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9) Find the remainder when 52021 is divided by 6.
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10) What is the remainder when 27557 is divided by 29?
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11) What is the largest power of 135 that perfectly divides 200!?
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12) What is the last digit of (4347× 17378) - (56234 + 48980)?
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13) What are the last 2 digits of 239448?
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14) How many different ordered pairs (a,b) exist such that a2−b2=324 where a and b are integers?
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15) In how many ways can 450 be written as the sum of 2 or more consecutive natural numbers?
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16) a=32+33+...+348. What is the remainder when a is divided by 13?
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17) How many consecutive zeroes are there at the end (i.e. right-most end) of the integer 2500250+2502500?
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18) How many consecutive zeroes are there at the end (i.e. right-most end) of 400!?
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19) What are the last two digits of 7575+8585+71233?
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20) Where n is a natural number, which of the following can never be the number of consecutive zeroes at the right-most end of n!?
(1) 26
(2) 28
(3) 29
(4) 31
Solution
1) 1
2) 18
3) 0
4) 36
5) 8
6) 123
7) 340
8) 8
9) 5
10) 14
11) 32
12) 1
13) 81
14) 10
15) 8
16) 10
17) 500
18) 99
19) 11
20) (3) 29
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